There are eleven different times in twelve hours when the hour and
minute hands of a clock are exactly one above the other. If we divide 12
hours by 11 we get 1 hr. 5 min. 27+3/11 sec., and this is the time after
twelve o'clock when they are first together, and also the time that
elapses between one occasion of the hands being together and the next.
They are together for the second time at 2 hr. 10 min. 54+6/11 sec.
(twice the above time); next at 3 hr. 16 min. 21+9/11 sec.; next at 4
hr. 21 min. 49+1/11 sec. This last is the only occasion on which the two
hands are together with the second hand "just past the forty-ninth
second." This, then, is the time at which the watch must have stopped.
Guy Boothby, in the opening sentence of his _Across the World for a
Wife_, says, "It was a cold, dreary winter's afternoon, and by the time
the hands of the clock on my mantelpiece joined forces and stood at
twenty minutes past four, my chambers were well-nigh as dark as
midnight." It is evident that the author here made a slip, for, as we
have seen above, he is 1 min. 49+1/11 sec. out in his reckoning.